c. \( \frac{2}{5}-\frac{3}{5} \) Problem 5 A family goes to a restaurant. When the bill comes, this is printed at the bottom of it: \( -4 \frac{3}{8}-\left(-1 \frac{1}{4}\right) \) \[ \begin{array}{l}\text { Gratuity Guide For Your Convenience: } \\ 15 \% \text { would be } \$ 4.89 \\ 18 \% \text { would be } \$ 5.87 \\ 20 \% \text { would be } \$ 6.52\end{array} \]

It looks like you're working on a math problem that involves subtracting fractions and analyzing a restaurant bill with gratuity calculations. Let's break down each part to help you understand and solve them. --- ### **Part c: Subtracting Fractions** **Problem:** \[ \frac{2}{5} - \frac{3}{5} \] **Solution:** Since both fractions have the **same denominator**, you can subtract the numerators directly: \[ \frac{2}{5} - \frac{3}{5} = \frac{2 - 3}{5} = \frac{-1}{5} = -\frac{1}{5} \] **Answer:** \(-\frac{1}{5}\) --- ### **Problem 5: Understanding the Restaurant Bill and Gratuity** **Given:** \[ -4 \frac{3}{8} - \left(-1 \frac{1}{4}\right) \] **Gratuity Guide:** \[ \begin{array}{l} 15\% \text{ would be } \$4.89 \\ 18\% \text{ would be } \$5.87 \\ 20\% \text{ would be } \$6.52 \end{array} \] **Step-by-Step Solution:** 1. **Interpret the Bill Amounts:** - The negative signs likely indicate amounts owed or charges. - The expression \( -4 \frac{3}{8} - \left(-1 \frac{1}{4}\right) \) represents the total amount on the bill after adjustments. 2. **Convert Mixed Numbers to Improper Fractions:** \[ -4 \frac{3}{8} = -\left(\frac{4 \times 8 + 3}{8}\right) = -\frac{35}{8} \] \[ -1 \frac{1}{4} = -\left(\frac{1 \times 4 + 1}{4}\right) = -\frac{5}{4} \] 3. **Simplify the Expression:** \[ -\frac{35}{8} - \left(-\frac{5}{4}\right) = -\frac{35}{8} + \frac{5}{4} \] 4. **Find a Common Denominator to Combine the Fractions:** - The common denominator for 8 and 4 is **8**. \[ \frac{5}{4} = \frac{5 \times 2}{4 \times 2} = \frac{10}{8} \] \[ -\frac{35}{8} + \frac{10}{8} = \frac{-35 + 10}{8} = \frac{-25}{8} = -3 \frac{1}{8} \] 5. **Interpret the Result:** - The final amount is \( -3 \frac{1}{8} \). This likely means that after adjustments, the family owes an additional \$3.125. 6. **Understanding Gratuity:** The gratuity amounts provided correspond to different percentage rates of the bill. Here's how you can calculate gratuity based on the net amount. - **Net Bill Amount:** \$3.125 - **Calculating Gratuity:** - **15% Gratuity:** \[ 3.125 \times 0.15 = 0.46875 \approx \$0.47 \] - **18% Gratuity:** \[ 3.125 \times 0.18 = 0.5625 \approx \$0.56 \] - **20% Gratuity:** \[ 3.125 \times 0.20 = 0.625 \approx \$0.63 \] - **Note:** The gratuity amounts you provided (\$4.89, \$5.87, \$6.52) suggest that they are based on a larger bill amount. Ensure that the net bill amount used for gratuity calculations matches the context of these amounts. --- ### **Summary** - **Part c:** \[ \frac{2}{5} - \frac{3}{5} = -\frac{1}{5} \] - **Problem 5:** - Simplified Bill: \( -3 \frac{1}{8} \) (which may represent an additional amount owed) - Gratuity Calculation: Based on the net bill, calculate 15%, 18%, or 20% accordingly. If you have a specific question or need further clarification on any part of this problem, feel free to ask!